Add Polynomials

A. Find (7y2 + 2y – 3) + (2 – 4y + 5y2).

Horizontal Method

(7y2 + 2y – 3) + (2 – 4y + 5y2)

= (7y2 + 5y2) + [2y + (–4y) + [(– 3) + 2] Group like terms.

= 12y2 – 2y – 1 Combine like terms.

Add Polynomials

Vertical Method

Answer: 12y2 – 2y – 1

7y2 + 2y – 3

(+) 5y2 – 4y + 2

Notice that terms are in descending order with like terms aligned.

12y2 – 2y – 1

Add Polynomials

B. Find (4x2 – 2x + 7) + (3x – 7x2 – 9).

Horizontal Method

(4x2 – 2x + 7) + (3x – 7x2 – 9)

= [4x2 + (–7x2)] + [(–2x) + 3x] + [7 + (–9)] Group like terms.

= –3x2 + x – 2 Combine like terms.

Add Polynomials

Vertical Method

Answer: –3x2 + x – 2

Align and combine like terms.4x2 – 2x + 7

(+) –7x2 – 3x – 9

–3x2 + x – 2

A. A

B. B

C. C

D. D

A. –2x2 + 5x + 3

B. 8x2 + 6x – 4

C. 2x2 + 5x + 4

D. –15x2 + 6x – 4

A. Find (3x2 + 2x – 1) + (–5x2 + 3x + 4).

A. A

B. B

C. C

D. D

A. 5x2 + 3x – 6

B. 4x3 + 5x2 + 3x – 6

C. 7x3 + 5x2 + 3x – 6

D. 7x3 + 6x2 + 3x – 6

B. Find (4x3 + 2x2 – x + 2) + (3x2 + 4x – 8).

Subtract Polynomials

A. Find (6y2 + 8y4 – 5y) – (9y4 – 7y + 2y2).

Horizontal Method

Subtract 9y4 – 7y + 2y2 by adding its additive inverse.

(6y2 + 8y4 – 5y) – (9y4 – 7y + 2y2)

= (6y2 + 8y4 – 5y) + (–9y4 + 7y – 2y2)

= [8y4 + (–9y4)] + [6y2 + (–2y2)] + (–5y + 7y)

= –y4 + 4y2 + 2y

Subtract Polynomials

Vertical Method

Align like terms in columns and subtract by adding the additive inverse.

Answer: –y4 + 4y2 + 2y

8y4 + 6y2 – 5y

(–) 9y4 + 2y2 – 7y Add the opposite.

8y4 + 6y2– 5y

(+) –9y4 – 2y2 + 7y –y4 + 4y2 +

2y

Subtract Polynomials

Find (6n2 + 11n3 + 2n) – (4n – 3 + 5n2).

Answer: 11n3 + n2 – 2n + 3

Horizontal Method

Subtract 4n4 – 3 + 5n2 by adding the additive inverse.

(6n2 + 11n3 + 2n) – (4n – 9 + 5n2)

= (6n2 + 11n3 + 2n) + (–4n + 3 – 5n2 )

= 11n3 + [6n2 + (–5n2)] + [2n + (–4n)] + 3

= 11n3 + n2 –2n + 3

Subtract Polynomials

Vertical Method

Align like terms in columns and subtract by adding the additive inverse.

Answer: 11n3 + n2 – 2n + 3

11n3 + 6n2 + 2n + 0

(–) 0n3 + 5n2 + 4n – 3

Add the opposite.

11n3 + 6n2 + 2n + 0

(+) 0n3 – 5n2 – 4n + 311n3 + n2 – 2n + 3

A. A

B. B

C. C

D. D

A. 2x2 + 7x3 – 3x4

B. x4 – 2x3 + x2

C. x2 + 8x3 – 3x4

D. 3x4 + 2x3 + x2

A. Find (3x3 + 2x2 – x4) – (x2 + 5x3– 2x4).

A. A

B. B

C. C

D. D

A. 2y4 – 2y2 – 11

B. 2y4 + 5y3 + 3y2 – 11

C. 2y4 – 5y3 + 3y2 – 11

D. 2y4 – 5y3 + 3y2 + 7

B. Find (8y4 + 3y2 – 2) – (6y4 + 5y3 + 9).

Add and Subtract Polynomials

A. VIDEO GAMES The total amount of toy sales T (in billions of dollars) consists of two groups: sales of video games V and sales of traditional toys R. In recent years, the sales of traditional toys and total sales could be modeled by the following equations, where n is the number of years since 2000.

R = 0.46n3 + 1.9n2 + 3n + 19

T = 0.45n3 + 1.85n2 + 4.4n + 22.6

A. Write an equation that represents the sales of video games V.

Add and Subtract Polynomials

Find an equation that models the sales of video games V.

Subtract the polynomial for R from the polynomial for T.

video games + traditional toys = total toy sales

V + R = T

V = T – R

0.46n3 + 1.9n2 – 3n – 19

(–)0.45n3 + 1.85n2 – 4.4n – 22.6

–0.01n3 + 0.05n2 + 1.4n + 3.6

Add and Subtract Polynomials

Answer: V = –0.01n3 + 0.05n2 + 1.4n + 3.6

Add the opposite. 0.46n3 + 1.9n2 – 3n – 19

(+) –0.45n3 – 1.85n2 + 4.4n + 22.6

–0.01n3 + 0.05n2 + 1.4n + 3.6

Add and Subtract Polynomials

B. Use the equation to predict the amount of video game sales in the year 2009?

Answer: The amount of video game sales in 2009 will be 12.96 billion dollars.

The year 2009 is 2009 – 2000 or 9 years after the year 2000. Substitute 9 for n. V = –0.01(9)3 + 0.05(9)2 + 1.4(9) + 3.6

= –7.29 + 4.05 + 12.6 + 3.6= 12.96

A. A

B. B

C. C

D. D

A. 50x2 – 50x + 500

B. –50x2 – 50x + 500

C. 250x2 + 950x + 500

D. 50x2 + 950x + 100

A. BUSINESS The profit a business makes is found by subtracting the cost to produce an item C from the amount earned in sales S. The cost to produce and the sales amount could be modeled by the following equations, where x is the number of items produced.C = 100x2 + 500x – 300S = 150x2 + 450x + 200Find an equation that models the profit.

A. A

B. B

C. C

D. D

A. $500

B. $30

C. $254,000

D. $44,000

B. Use the equation 50x2 – 50x + 500 to predict the profit if 30 items are produced and sold.